Below is a GREAT explanation of how vectors and matrices actually work (I don’t like your textbook’s walk through of this topic…)
Read through, try some example problems, and ask questions as needed. This should be getting done in the downtime where I’m going over content that you already feel you understand.
I expect you to get up to page 52.
At the point that you are able to multiply matrices with vectors, please complete the following set of problems: Transformational Matrices on Vectors
When multiplying Matrices:
Think of the second matrix as a collection of column vectors.
Think of the first matrix as a transformer, or manipulator of each column vector in the second matrix, and do the transformation of each vector. Your resulting product is now the collection of transformed (column) vectors.
*If you know/get how to transform one vector by a matrix, multiplying matrices is really just transforming multiple vectors by the same matrix.